Answer Happy

Practice Fimeriation 16. f(x)=(t−2xir+4)a−5​ (19) f(a)=(v+5r23x​ (C) f(x)=n+3x2−3​f(−2),f00,f(5) 12. f(x)=(x+7y2x​ 2. f(t)=x+4x2−16​f(−2),f(0),f(4) 12. f(x)=y2−4x+1564​ 2f(x)=4−xx2−2x−3​⋅f(−1),f(4),f(6) 14. (x)=x2−13x+336​ Aunrion (7) f(x)=x−5x−2​ 4. {(t)=x−6x−3​ a. f(x)=(t−1)(x+3)x−4​ 414 CHAPTER 8 Rafionit Eagretionts, functoons, and Eqution 53. x+3x2−46​=xx+1​=4 EL. x2−4x2−8+2​+2x+3+4 31. x2+5x4x+30​+ 22. x7+6uy1​+w​= Q. x2−x2x2+xx2+4x−4x​= a4. 213x−5​ as. x5​= ?
(41.) 3x+103x+7​ 69. 2a+b4a2+2ab+b2​⋅8a3−b34a2−b2​ 42. 2x+52x+3​ cannot te uimpifified 70. b2−b−627a3−8b3​⋅3ac−2bc−3a+2bbc−b−3c+3​b+28a2+6ab+3b2​ 43. 16−x2x2−x−12​x+4x+3​ 44. 9−x2x2−7x+12​−x+31−4​ 71. 3z2−8z+510z2+13z−3​⋅25z2−10z+12z2−3z−2z+3​⋅4z2−915z2−28z+5​ 45. 3x2−7xy+2y2x2+3xy−10y2​3x−46x+5y−y​2x2+5xy−3y2x2+2xy−3y2​2x−yx−y​ 72. z2−492z2−2z−12​⋅2z2+5z+24z2−1​⋅2z2−7z+32z2−13z−7​z+722z+11​ (47. x2−4x3−8​x+2x2+2x+4​ 48. x2−1x3−1​x+1x2+x+1​ In Exercises 73-90, divide as indicated. 49. x+4x3+4x2−3x−12​x2−3 73. 7x+5​÷94x+20​244​ 74. 3x+1​÷73x+3​41​ 50. x−2x3−2x2+x−2​,x2+1 75. y−64​+7y−4240​107​ 76. y−57​+3y−1528​ 77. 15x2−2x​+5x−2​ 78. 15x2−x​÷5x−1​ SECTION 6.1 Rational Expressions and Functions: Multiplying and Dividing 415 62. (x2+4x−5)+x+7x2−25​x−3(x+7x−1)​ 103. Find (gf​)(x) and the domain of gf​, 62 y2−10y+25y2−4y−21​+y2−6y+5y2+2y−3​y−y−4y−7​ (fR​)(x)=−1−2(−8,−2)∪(−2,1)∪(f,=) 64. y2+3y−28y2+4y−21​+y2+4y−32y2+14y+48​y+6z−3​ 104. Find (fg​)(x) and the domain of fg​ 85. 4x2+2x+18x3−1​÷(x−1)2x−1​(x−1)(2x−1) (f1​)(x)=−x+221​−x−22(−∞,−2)∪(−2,f)∪(f,−1)1​ 66. x3−27x2−9​÷x2+3x+9x2+6x+9​x+31​ (67. x2+3xy+2y2x2−4y2​+x+yx2−4xy+4y2​x−2y1​ Application Exercises The rational function
Practice Exercises In Exercises 1-l6, perform the indicated operations. These 8. y2−25y2​+y2−2525−10y​y+5y−5​ exercises imvolve addition and subsraction when denominators are the same. Simplify the result, if possible. 9. 4x−33x​−4x−32x−1​4x−1x+1​ 1. 9x2​+9x4​3x2​ 10. 7x−43x​−7x−42x−1​7x−4x+1​ 2. 6x11​+6x4​215​ (11) x2+6x−7x2−2​−x2+6x−719−4x​x−11​ (3.) x−5x​+x−59x+3​x−511x+3​ 12. x2+x−6x2+6x+2​−x2+x−62x−1​xx+1​−2 4. x−3x​+x−311x+5​x−112x+5​ 13. 6y2+y−220y2+5y+1​−6y2+y−28y2−12y−5​24y+1​+1 5. x2+3xx2−2x​+x2+3xx2+x​x+x2x−1​ 14. y2−5y+4y2+3y−6​−y2−5y+44y−4−2y2​3+2 6. x2−5xx2+7x​+x2−5xx2−4x​1−52x+3​ 15. x2−y22x3−3y3​−x2−y2x3−2y3​y3+x+y+y3 (7.) y2−9y2​+y2−99−6y​y−3 16. y2−x24y3−3x3​−y2−x23y3−2x3​y2+xy+y2
It Exrcises 17-28, find the leas common denominator of the. nalionad expresaione: 39. y2−5y+63y+7​−y−33​6−5(y−2)11​ (7) 25x211​ and 35x14​ 40. y2−7y+122y+9​−y−32​(y−3)(y−4)11​ 12. 15x27​ and 24x9​ 41. x2+9x+18x2−6​−x+6x−4​+1 19. x−52​ and x2−253​(x−5)(x+5) 42. x2+3x−10x2−39​−x−2x−7​=x+32​ 20. x+32​ and x2−95​(1+3x+−3) (43.) x2+7x+124x+1​+x2+5x+42x+3​(1+1kx+4x+3)6x2+14x+10​ 21. y2−1007​ and y(y−10)13​y(x+10)(y−10) 44. x2−x−63x−2​+x2−94x−3​4+3(x−3)(x+2)72+12x−12​ 22. y2−47​ and y(y+2)15​ 45. x2−x−2x+4​−x2+2x−82x+3​−(0+4x+2kx+1)x2−1x−13​ 23. x2−168​ and x2−8x+16x​(x+4)(x−4)(x−4) 46. x2−7x+62x+1​−x2−5x−6x+3​(x−5)(x+1)(x−1)y3+x+4​ 24. x2−253​ and x2−10x+25x​(x+5)(x−5)(x−5) 47. 4+x−31​x−34x−11​ (25.) y2−5y−6 and y2−4y−5y​(y−5)(y−6)(y+1) 48. 7+x−51​x−57x−4​ 27. 2y2+7y+67y​,y2−43​ and 2y2−3y−2−7y​ 49. y2−16y−7​+16−y27−y​(y+4)(y−4)2y−14​ 50. y2−25y−3​+25−y2y−3​ 28. y2−95y​,y2+6y+98​, and 2y2+5y−3−5y​ 51. 3x+6x+7​+4−x2x​x(x+2x−2)x2+2x−14​ In Exercises 20-66, perform the indicated operations, These 52. 4x+12x+5​+9−x2x​4(5−1)4−3​ etercises involve adduition and subtraction when denominators are different. Simplify the reselt, if possible. (53) x−42x​+x2−1664​−x+42x​=x−416​ (20) 5x23​+x10​4x23+51x​ 54. x−3x​+x2−2x−3x+2​−x+14​x+16x−3yx2−2x+14​ 30. 2x27​+x4​x27+xr​ 55. x2−y25x​−y−x7​x2−y213x+7y​ 31. x−24​+x+13​(x−2)(x+1)7x−2​ 56. x2−y29x​−y−x10​x2−y218x+10y​ 32. x−32​+x+27​(0−3)(x+2) (57) 5x+63​−x−24​+5x2−4x−12x2−x​84+6(x−2)x2−the−30​ 33. x2+x−23x​+x2−4x+32​(x+2xx−113x−4​ 58. x2+2x+1x−1​−2x−23​+x2−1x​2x+16x+1)(x−1x2−16−1​ 34. x2+2x−87x​+x2−3x+23​(x+4)(x−2)(x−1) 59. x2−9xy+20y23x−y​+x2−25y22y​(1+5,4x−5,4x−4x2+1e2) 35. x+5x−6​+x−6x+5​(1+5)(x−6)2x2−2x+6)​ 36. x+7x−2​+x−2x+7​11+7hx−21x2+16x+53​ 60. x2+4xy+4y2x+2y​−x2−4y22x​−x−2y1​ 61. x2−43x​+x2+x−25x​−x2−4x+43​
Practice Exercises In Exercises 1−40, simplify each complex rational expression by the method of your choice. 11. 5x+51​−x1​​−x(x+5)1​ 12. 6x+61​−x1​​−x(x+6)1​ (1.) 1−x3​4+x2​​1−341+2​ 2. 3+x1​5−x2​​3+15x−2​ 13. x+41​−x1​x+44​​ 14. x+71​−x1​x+77​​ 3. 3x​−x3​x3​+3x​​(x−3)(x+3)x2+4​ 4. 51​+x1​5x​−x5​​,=5 15. x+11​−1x−11​+1​−x−11​ 16. x−11​+1x+11​−1​−x+1x−1​ (5.) x1​−y1​x1​+y1​​y−1y+1​ 17. (x+y)−1x−1+y−1​xy(4+y(x+y)​ 6. xy​+x1​yx​+x1​​x+11x2+y​ 18. (x−1+y−1)−11+yxy​ 7. 10x−1−6x−28x−2−2x−1​5x−34−x​ 8. 15x−1−9x−212x−2−3x−1​4x−34−x​ 19. x+2x−2​+x−2x+2​x−2x+2​−x+2x−2​​ 20. x+1x+1​+x−1x+2​x−1x+1​−x+1x−1​​x2x2+x+3​ 9. 1−x−21​x−21​​x−31​ 10. 1+x+21​x+21​​+1+11​ 21. x3y5​−xy3​x3y2​+xy45​​ (4) 22. x2y1​+xy32​xy23​+x2y2​​
30. y−33​+y−22​y2−5y+65y​​ sy 31. a21​−ab3​+b22​+2x−20a22​−ab1​−b21​​ 45. 1−1+x1​1​1​ 35. x2+2xy3y​+x5​x+2y3​−x2+2xy2y​​13y+3414−2y​ In Exerises 47−48, fet f(x)=1−x1+x​, 47. Find f(x+31​) and simplify. x+2x+4​ 48. Find f(x−61​) and simplify. := ? 36. x−y1​−x2+xy+y21​x3−y31​​y2+x+y2−1+y1​ In Exercises 49-50, use the given rational function to find and simplify 37. m2−12​+m2+4m+3m(m+3)​m2−m−22​m2−3m+2​​(m−2)m−2nm+11​ hf(a+h)−f(a)​
Practice Exercises In Exercises 13-36, divide as indicated. Check at least five of In Exercises 1-12, divide the polynomial by the monountal. Your answers by showing that she product of the divisor and the (1. 5x325x7−15x5+10x3​5x4−x2+2 (13.) (x2+8x+15)+(x+5)=3 2. 7x349x7−28x5+14x3​−7x4−4x2+2 14. (x2+3x−10)+(x−2)+5 3. 3x18x3+6x2−9x−6​x2+2x−3−42​ 15. (x3−2x2−5x+6)÷(x−3)x2+x−2 4. 5x25x3+50x2−40x−10​+x2+60x−8−x2​ 16. (x3+5x2+7x+2)+(x+2)x2+34+1 (5.) (28x3−7x2−16x)+(4x2)+7−47​−14​ 17. (x2−7x+12)÷(x−5)x−2+x−52​ 6. (70x3−10x2−14x)+(7x2) ine −710​−22​ 18. (2x2+x−9)÷(x−2)2x+5+x−21​ 7. (25x8−50x7+3x6−40x5)+(−5x5) 19. (2x2+13x+5)+(2x+3)+5−2x+316​ −5x2+40x2−53​x+3 20. (8x2+6x−25)+(4x+9)2x−3+4r+92​ 8. (18x7−9x6+20x5−10x4)÷(−2x4) 21. (x3+3x2+5x+4)+(x+1)x3+2x+3+x+11​ −9x3+24​x7−16x+5 22. (x3+6x2−2x+3)+(x−1)x2+7x+5+x−15​ 9. (18a3b2−9a2b−27ab2)÷(9ab)≥a2b−a−16 23. (4y3+12y2+7y−3)+(2y+3)2y2+3y−1 10. (12a2b2+6a2b−15ab2)+(3ab)ab+2a−5b 24. (6y3+7y2+12y−5)+(3y−1)2y2+3y+5 25. (9x3−3x2−3x+4)+(3x+2) 342−3+1+162​+3
49. x−3y4x3−7x3y−16ay2+3y3​ 6r +40y 34. (4y4−17y2+14y−3)+(2y−3)+2y4+1y−2+4+1 60. 4x−5y12x3−19x2y+13ry2−10y3​ (33. (4x4+3x3+4x2+9x−6)+(x2+3) In Euercites 51-52 fond (hf−g​)(x) and the donnain of  34. (3x3−x1+4x2−12x−8)+(x2−2)​ 51. f(x)=3x3+4x2−x−4.(x)=−5x3+22x2−24x−2x​ 35. (15x4+3x3+4x2+4)+(3x2−1)+3x1+x+3+8+7 3n 52. f(x)=x3+9x2−6x+25,5(x)=−3x3+2x2−14x 37. f(x)=8y3−38x2+49x−10. simplify. 54. ax −3x+6=a3−6a2+11ay=e2−40−2 33. f(x)=2x3−9x2−17x+39. g(x)=2x−3(1)(n=1+−4−13 Application Exercises 39. f(x)=2x4−7x3+7x2−9x+10, g(x)=2x−5(f)(x)=,x′+x−2f(x)=x−11080t−800​,300x≤100 Rewrite the function by using long division to perfort  44. x2−3x−2x4−x3−7x2−7x−2​​ you obtain the same answer as you did in Excrioe  Which form of the functioa do you find eacer to ​ you obtain the same answet as yoe did in 1 setcoe Which form of the functioa do yow find easicr to ese"
wo ciercises, begin the provess as shown. 26. f(x)=6x4+10x3+5x2+x+1 : f(−32​) 4. (5x2−12x−8)+(x+3)-x −27=7 5. (4x3−3x2+3x−1)+(x−1) 4x- * s 6. (5x3−6x2+3x+11)+(x−2) 7. (6x3−2x3+4x2−3x+1)÷(x−2) (27) x3−4x2+x+6=0,−1 8. (x3+4x4−3x2+2x+3)+(x−3) 29. 2x3−5x2+x+2=0,2 x4+7x3+21v2+ ARA =1ke+1−734​ 30. 2x3−3x2−11x+6=0x−2 2. (x2−5x−5x3+x4)+(5+x) (31) 6x3+25x2−24x+5=0x−5 32. 3x3+7x2−22x−8=0;−4 pot'momial equation (17) (3x3+2x2−4x+1)+(x−31​)42+3x−3 12. (2x4−x3+2x2−3x+1)+(x−21​)≥x+2x−5= 12. x−1x4+x3−2​y2+y2+y4+2y+2 14. x+2x7+x5−10x3+12​ 33. x3+2x2−5x−6=0 (15) x−4x4−256​+2 *r + is =14 34. 2x3+x2−13x+6=0 17. x+22x5−3x4+x3−x2+2x−1​ 18. x−2x3−2x4−x3+3x2−x+1​+x4−x2+x+1+x−23​
In Exercises 1-34, solve each rational equation. If an equation has no solution, so state. 12. x−43x+1​=2x−76x+5​ ne sulatiin of Q 1. x1​+2=x3​ (13.) 1−x+74​=x+75​ 14. 5−x−52​=x−53​ 2. x1​−3=x4​∣−1∣ 15. x+24x​+x−12​=4 ∣2∣} 3. x5​+31​=x6​ 16. x+13x​+x−24​=3 |-10| 4. x4​+21​=x5​ 17. x2−98​+x+34​=x−32​ (5.) 2xx−2​+1=xx+1​ 18. x2−2532​=x+54​+x−52​ (31) 6. 5x7x−4​=59​−x4​ 19. x+x7​=−8∣−7,−1∣ 7. x+13​=x−15​∣−4∣ 20. x+x6​=−7∣−6,−1∣ 8. x+36​=x−34​ [15] (21.) x6​−3x​=1(−6,3) 9. x+5x−6​=x+1x−3​ 22. 2x​−x12​=1(−4,0)
(25) x−11​+x+11​=x2−12​ nen solation or 2 46. x3−12​+(x−1)(x2+x+1)4​+x2+x+11​ 26. x−21​+x+21​=x2−44​ eosinuser or Q (31.) x+45​+x+33​=x2+7x+1212x+19​ In Exercises 47-48, find all values of a for which 29. x2+2x−82x−1​+x+42​=x−21​ f(a)=g(a)+1. 47. f(x)=x+3x+2​,g(x)=x2+2x−3x+1​ 29. x+34x​−x−312​=x2−94x2+36​ 48. f(x)=x−34​⋅g(x)=x4+x−1210​−1,6 30. x+32​−x+15​=x2+4x+33x+5​ In Exercises 49−50, find all values of a for which or is (31) x2+3x−104​+x2+9x+201​=x2+2x−82​(43​) (f+g)(a)=h(a). 49. f(x)=x−45​,g(x)=y−x3​,h(x)=x2−7x+13x2−20​
(1.) f(x)=x+3x2−9​;f(−2),f(0),f(5) 2. f(x)=x+4x2−16​;f(−2),f(0),f(5) 3. f(x)=4−xx2−2x−3​;f(−1),f(4),f(6) 4. f(x)=3−xx2−3x−4​;f(−1),f(3),f(5) 5. g(t)=t2+12t3−5​;g(−1),g(0),g(2) 6. g(t)=t2+42t3−1​;g(−1),g(0),g(2) In Exercises 7-16, find the domain of the given rational function. 7. f(x)=x−5x−2​
11. f(x)=(x+5)22x​ 12. f(x)=(x+7)22x​ 13. f(x)=x2−8x+153x​ 14. f(x)=x2−13x+363x​ 15. f(x)=3x2−2x−8(x−1)2​
In Exercises 27-50, simplify each rational expression. If the rational expression cannot be simplified, so state. 27. x−2x2−4​ 28. x−5x2−25​ 29. x2−x−6x+2​ 30. x2−2x−3x+1​ 31. x2+5x4x+20​ 32. x2+6x5x+30​ 33. y2−254y−20​ 34. y2−496y−42​ 35. 25−9x23x−5​ 36. 4−25x25x−2​ 37. y2−14y+49y2−49​ 38. y2−6y+9y2−9​ 39. x2−3x+2x2+7x−18​ 40. x2+5x+4x2−4x−5​ 41. 3x+103x+7​ 42. 2x+52x+3​ 43. 16−x2x2−x−12​ 44. 9−x2x2−7x+12​ 45. 3x2−7xy+2y2x2+3xy−10y2​ 46. 2x2+5xy−3y2x2+2xy−3y2​ 47. x2−4x3−8​ 48. x2−1x3−1​
In Exercises 51-72, multiply as indicated. 51. x+7x−3​⋅2x−63x+21​ 52. x+3x−2​⋅5x−102x+6​ 53. x2−4x−21x2−49​⋅xx+3​ 54. x2−3x−10x2−25​⋅xx+2​ 55. x2−x−6x2−9​⋅x2+x−6x2+5x+6​ 56. x2−4x2−1​⋅x2−2x−3x2−5x+6​ 57. x2+8x+16x2+4x+4​⋅(x+2)3(x+4)3​ 58. x2−4x+4x2−2x+1​⋅(x−1)3(x−2)3​ 59. y2−98y+2​⋅4y2+y3−y​ 60. y2−16y+2​⋅3y2+y1−y​ 61. y2−4y3−8​⋅2yy+2​ 62. y3+27y2+6y+9​⋅y+31​ 63. (x−3)⋅x2−5x+6x2+x+1​ 64. (x+1)⋅x2+7x+6x+2​ 65. x2−y2x2+xy​⋅x4x−4y​ fr x2−y2x2+xy
69. 2a+b4a2+2ab+b2​⋅8a3−b34a2−b2​ 70. b2−b−627a3−8b3​⋅3ac−2bc−3a+2bbc−b−3c+3​ 71. 3z2−8z+510z2+13z−3​⋅25z2−10z+12z2−3z−2z+3​⋅4z2−915z2−28z​ 72. z2−492z2−2z−12​⋅2z2+5z+24z2−1​⋅2z2−7z+32z2−13z−7​ In Exercises 73-90, divide as indicated. 73. 7x+5​÷94x+20​ 74. 3x+1​÷73x+3​
87. x2+3xy+2y2x2−4y2​÷x+yx2−4xy+4y2​
In Exercises 103-104, let f(x)=1−2x(x+2)2​ and g(x)=2x−1−x+2​. 103. Find (gf​)(x) and the domain of gf​.
6.2 EXERCISE SET MyMathLab Practice Exercises In Exercises 1-16, perform the indicated operations. These exercises involve addition and subtraction when denominators are the same. Simplify the result, if possible. 1. 9x2​+9x4​ 2. 6x11​+6x4​ 3. x−5x​+x−59x+3​ 4. x−3x​+x−311x+5​ 5. x2+3xx2−2x​+x2+3xx2+x​ 6. x2−5xx2+7x​+x2−5xx2−4x​ 7. y2−9y2​+y2−99−6y​
(11.) x2+6x−7x2−2​−x2+6x−719−4x​
In Exercises 17-28, find the least common denominator of the rational expressions. (17.) 25x211​ and 35x14​ 18. 15x27​ and 24x9​ 19. x−52​ and x2−253​ 20. x+32​ and x2−95​ 21. y2−1007​ and y(y−10)13​ 22. y2−47​ and y(y+2)15​ 23. x2−168​ and x2−8x+16x​ 24. x2−253​ and x2−10x+25x​ 25. y2−5y−67​ and y2−4y−5y​
In Exercises 29-66, perform the indicated operations. These exercises involve addition and subtraction when denominators are different. Simplify the result, if possible. 29. 5x23​+x10​ 30. 2x27​+x4​ 31. x−24​+x+13​ 32. x−32​+x+27​ 33. x2+x−23x​+x2−4x+32​ 34. x2+2x−87x​+x2−3x+23​ 35. x+5x−6​+x−6x+5​ 36. x+7x−2​+x−2x+7​ 37. x2−253x​−x+54​
43. x2+7x+124x+1​+x2+5x+42x+3​
53. x−42x​+x2−1664​−x+42x​ 54. x−3x​+x2−2x−3x+2​−x+14​ 55. x2−y25x​−y−x7​ 56. x2−y29x​−y−x10​ 57. 5x+63​−x−24​+5x2−4x−12x2−x​
In Exercises 1-40, simplify each complex rational expression by the method of your choice. 1. 1−x3​4+x2​​ 2. 3+x1​5−x2​​ 3. 3x​−x3​x3​+3x​​ 4. 51​+x1​5x​−x5​​ (5. x1​−y1​x1​+y1​​ 6. xy​+x1​yx​+x1​​ 7. 10x−1−6x−28x−2−2x−1​ 8. 15x−1−9x−212x−2−3x−1​ 9. 1−x−21​x−21​​ 10. 1+x+21​x+21​​
x3y5​−xy3​x3y2​+xy45​​
y+31​+y+12​y2+4y+32y​​
In Exercises 47-48, let f(x)=1−x1+x​. 47. Find f(x+31​) and simplify. 48. Find f(x−61​) and simplify. In Exercises 49-50, use the given rational function to find and simplify hf(a+h)−f(a)​ 49. f(x)=x3​
Practice Exercises In Exercises 1-12, divide the polynomial by the monomial. (1.) 5x325x7−15x5+10x3​ 2. 7x349x7−28x5+14x3​ 3. 3x18x3+6x2−9x−6​ 4. 5x25x3+50x2−40x−10​ 5. (28x3−7x2−16x)÷(4x2) 6. (70x3−10x2−14x)÷(7x2) 7. (25x8−50x7+3x6−40x5)÷(−5x5) 8. (18x7−9x6+20x5−10x4)÷(−2x4) 9. (18a3b2−9a2b−27ab2)÷(9ab)
In Exercises 13-36, divide as indicated. Check at least five of your answers by showing that the product of the divisor and the quotient, plus the remainder, is the dividend. 13. (x2+8x+15)÷(x+5) 14. (x2+3x−10)÷(x−2) 15. (x3−2x2−5x+6)÷(x−3) 16. (x3+5x2+7x+2)÷(x+2) 17. (x2−7x+12)÷(x−5) 18. (2x2+x−9)÷(x−2) 19. (2x2+13x+5)÷(2x+3) 20. (8x2+6x−25)÷(4x+9) 21. (x3+3x2+5x+4)÷(x+1) 22. (x3+6x2−2x+3)÷(x−1) 23. (4y3+12y2+7y−3)÷(2y+3) 24. (6y3+7y2+12y−5)÷(3y−1) 25. (9x3−3x2−3x+4)÷(3x+2)
29. (4y3−5y)÷(2y−1) 30. (6y3−5y)÷(2y−1) 31. (4y4−17y2+14y−3)÷(2y−3) 32. (2y4−y3+16y2−4)÷(2y−1) 33. (4x4+3x3+4x2+9x−6)÷(x2+3)
Practice PLUS In Exercises 41-50, divide as indicated. 41. x+yx4+y4​ 42. x+yx5+y5​ 43. x2+x+23x4+5x3+7x2+3x−2​ 44. x2−3x−2x4−x3−7x2−7x−2​ 45. x2+x+14x3−3x2+x+1​ 46. x2+x+1x4−x2+1​ 47. x2−x+2x5−1​
MyMathLab° Practice Exercises In Exercises 1-18, divide using synthetic division. In the first two exercises, begin the process as shown. 1. (2x2+x−10)÷(x−2)221−10 2. (x2+x−2)÷(x−1) 1] 1 1 −2 3. (3x2+7x−20)÷(x+5) 4. (5x2−12x−8)÷(x+3) 5. (4x3−3x2+3x−1)÷(x−1) 6. (5x3−6x2+3x+11)÷(x−2) 7. (6x5−2x3+4x2−3x+1)÷(x−2) 8. (x5+4x4−3x2+2x+3)÷(x−3) 9. (x2−5x−5x3+x4)÷(5+x) 10. (x2−6x−6x3+x4)÷(6+x) 11. (3x3+2x2−4x+1)÷(x−31​) 12. (2x4−x3+2x2−3x+1)÷(x−21​) 13. x−1x5+x3−2​ 14. x+2x7+x5−10x3+12​ 15. x−4x4−256​
In Exercises 19-26, use synthetic division and the Remainder Theorem to find the indicated function value. 19. f(x)=2x3−11x2+7x−5;f(4) 20. f(x)=x3−7x2+5x−6;f(3) 21. f(x)=3x3−7x2−2x+5;f(−3) 22. f(x)=4x3+5x2−6x−4;f(−2) 23. f(x)=x4+5x3+5x2−5x−6;f(3) 24. f(x)=x4−5x3+5x2+5x−6;f(2)
In Exercises 27-32, use synthetic division to show that the number given to the right of each equation is a solution of the equation. Then solve the polynomial equation. 27. x3−4x2+x+6=0;−1 28. x3−2x2−x+2=0;−1 29. 2x3−5x2+x+2=0;2 30. 2x3−3x2−11x+6=0;−2 31. 6x3+25x2−24x+5=0;−5